Although modeling of spatial-temporal stochastic processes is a growing area of research, one underdeveloped area in this field is the multivariate space-time setting. The motivation for this research originates from air quality studies. By treating each air pollutant as a separate variable, the multivariate approach will enable modeling of not only the behavior of the individual pollutants but also the interaction between pollutants over space and time. Studying both the spatial and the temporal aspects of the process gives a more accurate picture of the behavior of the process. A bivariate state-space model is developed and includes a covariance function which can account for the different cross-covariances across space and time. The Kalman filter is used for parameter estimation and prediction. The model is evaluated through the prediction efforts in an air-quality application.